Definitions for maximum likelihood
max·i·mum like·li·hood

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1. maximum likelihood

   In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when all observed outcomes are assumed to have normal distributions with the same variance.From the perspective of Bayesian inference, MLE is generally equivalent to maximum a posteriori (MAP) estimation with uniform prior distributions (or a normal prior distribution with a standard deviation of infinity). In frequentist inference, MLE is a special case of an extremum estimator, with the objective function being the likelihood.

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1. Maximum likelihood

   In statistics, maximum-likelihood estimation is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximum-likelihood estimation provides estimates for the model's parameters. The method of maximum likelihood corresponds to many well-known estimation methods in statistics. For example, one may be interested in the heights of adult female penguins, but be unable to measure the height of every single penguin in a population due to cost or time constraints. Assuming that the heights are normally distributed with some unknown mean and variance, the mean and variance can be estimated with MLE while only knowing the heights of some sample of the overall population. MLE would accomplish this by taking the mean and variance as parameters and finding particular parametric values that make the observed results the most probable. In general, for a fixed set of data and underlying statistical model, the method of maximum likelihood selects the set of values of the model parameters that maximizes the likelihood function. Intuitively, this maximizes the "agreement" of the selected model with the observed data, and for discrete random variables it indeed maximizes the probability of the observed data under the resulting distribution. Maximum-likelihood estimation gives a unified approach to estimation, which is well-defined in the case of the normal distribution and many other problems. However, in some complicated problems, difficulties do occur: in such problems, maximum-likelihood estimators are unsuitable or do not exist.

How to pronounce maximum likelihood?

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How to say maximum likelihood in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of maximum likelihood in Chaldean Numerology is: 9

2. Pythagorean Numerology

   The numerical value of maximum likelihood in Pythagorean Numerology is: 5

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Maximum_Likelihood
2. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=maximum likelihood